Asset Pricing Experiments: Bubbles, Crashes & Expectations

Transcription

1 Asset Pricing Experiments: Bubbles, Crashes & Expectations John Du y U. Pittsburgh BLEESSM June 2011 Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

2 Asset Price Bubbles A bubble is di cult to de ne, but it involves seemingly irrational behavior and is manifested by a sustained departure of the price of an asset from underlying fundamentals. Bubbles are typically viewed as unsustainable, though examples of stationary bubbles, e.g. at money, have been provided (Tirole Ecmta 1985). The supposed irrationality underlying asset price bubbles has been thoroughly questioned, as it challenges the e cient markets hypothesis. This has led to theories of rational bubbles. However, as these rational bubble theories appear at odds with the actual volatility in asset prices, as well as with laboratory evidence showing that individuals are not invariant to the decision-frame, a new behavioral nance literature has emerged to challenge the conventional view of asset pricing. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

3 Rational Bubbles Perhaps the main theory of bubbles is the rational bubble theory. De ne the gross rate of return on an asset R t+1 = p t+1 + d t+1 p t so the net return r t+1 = R t 1, with p t being the price in period t and d t the dividend. Rearranging and taking expectations conditional on date t information, we have p t = E t(p t+1 + d t+1 ) 1 + E t (r t+1 ) Assuming rational expectations and that E t (r t+1 ) = r, the rate of time preference, we can write: p t = (1 + r) 1 E t (d t+1 + p t+1 ). (1) Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

4 Rational Bubbles, Continued Using the law of iterated expectations, we can expand the price equation as: p t = n i=1 Taking the limit as n goes to in nity: p t = i=1 (1 + r) i E t (d t+i ) + (1 + r) n E t (p t+n ). (1 + r) i E t (d t+i ) + lim (1 + r) n E t (p t+n ), n! assuming the limit exists. Call the rst term the fundamental component f t and the second term the bubble component, b t, p t = f t + b t (2) Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

5 Properties of Rational Bubbles Substitute (2) into (1): Using the de nition of f t : i=2 f t + b t = (1 + r) 1 E t (d t+1 + f t+1 + b t+1 ) i=1 (1 + r) i E t (d t+i ) + b t = (1 + r) 1 E t (d t+1 ) + (1 + r) i E t (d t+i ) + (1 + r) 1 E t (b t+1 ) or b t = (1 + r) 1 E t (b t+1 ) Rational bubbles grow at the same rate as fundamentals: if b > 0, prices grow exponentially. Rational bubbles can occur only in models with an in nite horizon, otherwise by backward induction b T = 0 implies b t = 08t! If there is a constant probability that a bubble will burst it must grow at an even faster rate to compensate. (Blanchard and Watson 1982). Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

6 Bubbles in the Laboratory?: Non-rational bubbles Smith Suchaneck and Williams (SSW, Ecmta 1988) experimental design reliably generates asset price bubbles and crashes in a nite horizon economy, thus ruling out rational bubble stories. T trading periods (typically T = 15) and 9-12 inexperienced subjects. Each subject is initially endowed with various amount of cash and assets. Assets are long-lived (T periods). Endowments, are ex-ante identical in expected value -there is no reason for trade! In each trading period, agents are free to buy or sell the asset. Trade takes place via a double auction, and bids and asks must obey standard improvement rules. For each unit of the asset held at the end of a trading period, the asset owner earns a dividend payment which is a uniform draw from a known distribution and has mean d. It is public knowledge that the fundamental value of an asset at the start of period t is given by: D T t = d(t t + 1) + D T T +1. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

7 An Speci c Parameterization (SSW Design #2) Payo = initial endowment of money+dividends on assets held+money received from sales of shares- the money spent on purchases of shares+buyout value. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

8 Bubbles and Crash Phenomenon Illustrated Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

9 Bubbles Often Disappear With Experienced Subjects (Two 15 Round Sessions) Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

10 Data Analysis There is a substantial volume of bids, asks and trading volume in this type of experiment Smith et al. analyze a price adjustment dynamic of the form: P t P t 1 = α + β(b t O t ) where P t is mean traded price in period t, B t is the number of bids in period t and O t is the number of asks in period t. The rational, e cient markets hypothesis is that α = E t d t and β = 0, i.e., that subjects are trading according to fundamentals. Empirically, Smith et al. report that they cannot reject that hypothesis that α = E t d t but they do nd that β is signi cantly positive: B t O t captures variations in aggregate demand, which a ects prices. Conclude that a common dividend and common knowledge of it are insu cient to generate common expectations among inexperienced subjects. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

11 Robustness of Laboratory Bubbles? Smith et al. (ET 2000) show that the bubble crash pattern persists if dividends are eliminated, and there is only a nal buy-out value. Noussair et al. (EE 2001) show that bubbles continue to emerge if there is a constant (non-decreasing) dividend value. They suppose that dividends are a uniform random draw from the set f.03,.02, 0.005, 0.045g, so d = 0. They report that in 4 out of 8 sessions, they get a bubble crash pattern as in the Smith et al. design. Dufwenberg et al. (AER 2005) show that adding just a small fraction of experienced traders - 1/3 with 2/3 inexperienced leads to a near elimination of bubbles. Haruvy and Noussair (JFin 2006) argue that the restriction on short-sales may lie behind departures from fundamentals. In the absence of short sales, a trader s ability to speculate on downward price movements is limited to the sale of all the assets he owns. They nd that relaxing short-sale restrictions can reduce prices. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

12 Lei et al. (Ecmta 2001) Explore the boredom/experimenter demand hypothesis They consider two main treatment variables. No-Spec treatment: Buyers and Sellers have distinct roles. In particular, a buyer cannot resell his asset later in a 2-minute trading period at a higher price. This tests the greater-fool hypothesis that speculation is driving the results. Two-Market treatment: Two markets operate simultaneously. One is for a one-period asset Y; holders of this asset sell it to buyers in xed roles. The other market is the standard 15-period asset of the laboratory bubble design; this asset could be traded (bought and sold) by all subjects. Main nding, neither treatment completely eliminates bubbles and crashes. Trading volume is much lower in the two-market treatment as compared with the standard one-market case. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

13 Lei et al. s ndings NoSpec/Spec illustrated Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

14 Haruvy et al. (AER 2007) Look at role of long-term expectations in the SSW design. At the start of each trading period, t< T=15, elicit trader s expectations of market prices in all remaining T-t+1 periods. Used a call-market institution, a sealed-bid version of a double auction: each trader can submit a buy or sell price and a quantity to buy/sell. Bids are ranked from highest to lowest, asks from lowest to highest and a single market price is determined. 9 Subjects participate together in 4, 15-period "markets" (replications). Subjects were paid both for trades and correct market price predictions. Clear evidence that inexperienced subjects have incorrect beliefs about the correspondence between prices and fundamentals. Price predictions are adaptive: market peaks consistently occur earlier than traders predict. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

15 Prices and Beliefs About Prices Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

16 Repeated Bubbles and Crashes with Experienced Subjects? Hussam et al. AER 2008 argue that repeated bubbles among experienced subjects requires a change in the asset environment as might arise e.g., from a technological revolution. They rst run 5 cohorts of 9-12 subjects through a standard SSW experimental design. In a new rekindle treatment, they take once-experienced subjects and: 1) randomly divide them into 3 new groups (so group composition is altered). They also 2) increase the mean and variance of the dividend process the support changes from {0, 8, 28, 60} to {0,1,28,98} and nally 3) they cut initial share endowments in half and double the initial cash positions of the three player types. This rekindle treatment is compared with a standard "twice-repeated" treatment with no change in the subject population, dividend process or initial conditions. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

17 Shocking the system leads to bubbles among experienced subjects Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

18 A Forecasting Game Approach to Asset Pricing (Hommes et al. 2005) 6 subjects seek to forecast the price of an asset. They can condition on past prices (except for the rst period). The dividend per unit of asset is a known constant d (alternatively, can be stochastic with known distribution). No other task: given the 6 forecasts, actual prices are determined by a computer program using p t = r! pi,t+1 e + d + ɛ t. i=1 where ɛ t is a mean zero stochastic process. This is a pure test of expectation formation; no confounding e ects from trading behavior. Payo s are according to forecast accuracy. Rational expectation prediction is p t = d/r+ ɛ t /r. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

19 Findings Monotonic and Oscillatory Convergence/Divergence are all observed. Often there is excess volatility relative to ɛ which is very small. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

20 Summary Participants who succeed in predicting average opinion well perform well in this experiment. This feature may be similar to real asset markets and is support for Keynes famous beauty contest analogy. Subjects are rather successful in anticipating what "average opinion expects average opinion to be." They also consider a variant where some fraction of traders are programmed to predict the fundamental price in every period; this further helps convergence to some degree. But restriction of prices to (0,100), though this range includes the fundamental price, rules out rational bubbles. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

21 A Consumption Smoothing GE Approach (Crockett and Du y 2010) Assets are potentially long-lived and pay a common dividend (in terms of francs) Francs (consumption) converted into dollars each period and then disappear. In nite horizon, implemented as a constant probability of continuation of a sequence of trading periods. We induce a utility function on subjects (the franc-to-dollar exchange rate) that is either concave or linear. If concave, there is an induced (smoothing) incentive for trade in the asset; If linear, there is no induced incentive for trade in the asset. We nd asset under-pricing (relative to the expected value) in the concave utility treatment, and asset bubbles in the linear utility treatment. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

22 Model The representative agent of type i seeks to maximize: subject to max E 1 fct i g β t 1 u i (c t=1 t i ), t=1 c i t = y i t + d t s i t p t s i t+1 s i t, y i t + d t s i t p t (s i t+1 s i t) 0, s i t 0. The rst order condition for each time t 1, suppressing agent superscripts for notational convenience, is: u p t = 0 (c t+1 ) βe t u 0 (c t ) (p t+1 + d). Steady state equilibrium price: p = concave and linear treatments. β 1 βd. Same for both the Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

23 Within-period Sequencing The timing of activity is summarized below: Begin period t. Income and dividends paid. Assets traded (3-minute double auction) Random draw against β determined by die roll. Begin period t + 1, if applicable. The set of periods that comprise the life" of a given asset is called a sequence. We run several sequences per session. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

24 Endowments and Treatments Endowments Type No. Subjects s1 i fyt i g = u i (c) = if t is odd, δ 1 + α 1 c φ1 44 if t is even if t is odd, δ 2 + α 2 c φ2 90 if t is even 2 2 Treatment Design d = 2 d = 3 Concave C2 C3 φ i < 1 and α i φ i > 0 4 sessions 4 sessions Linear L2 L3 φ i = 1 4 sessions 4 sessions Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

25 Steady State Competitive Equilibrium Benchmarks d = 2 d = 3 p = 10 Type 1 shares cycle between 1 (4) in odd (even) periods Type 2 shares cycle between 4 (1) in odd (even) periods p = 15 Type 1 shares cycle between 1 (3) in odd (even) periods Type 2 shares cycle between 4 (2) in odd (even) periods Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

26 Holt-Laury Paired Choice Lottery Beginning with session 7, subjects faced Holt-Laury (2002) paired-lottery task after the asset market experiment. Ten choices between two lotteries, A and B. A paid $6 or $4.80, B paid $11.55 or $0.30. In choice n 2 1, 2,...10, the probability of receiving the high payo was 0.1 n One choice was chosen for payment at random. Risk-neutral subject would choose B six times. 16% of subjects chose B at least six times, 30% chose B at least ve times, mean number of B choices was 3.9 (a common frequency in the literature) which implies a Coe of RRA 0.41<r<0.68 (moderate risk aversion). Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

27 Price Results Finding 1: In the concave utility treatment (φ i < 1), observed transaction prices at the end of the session are generally less than or equal to p = β d. (1 β) Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

28 Price Results Finding 1: In the concave utility treatment (φ i < 1), observed transaction prices at the end of the session are generally less than or equal to p = β d. (1 β) Finding 2: In the linear induced utility sessions (φ i = 1) trade in the asset does occur, at volumes similar to the concave sessions. Observed transaction prices are signi cantly higher in the linear sessions. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

29 Median Equilibrium-Normalized Prices Concave, d=2 Concave, d=3 Linear, d=2 Linear, d=3 Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

30 Prices Across Treatments Mean First Pd Final Half Final 5 Pds Final Pd Forecast Change Prob C S S S S C S S S S L S S S S L S S S S Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

31 Focus on nal prices Why? Rather complicated environment with potential for substantial learning. During the second half of sessions: Concave treatment prices trended at or down Linear treatment prices trended at or up. Final prices therefore best re ect learning and long-term trends. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

32 Analysis of Price Di erences Pooling by linear vs. concave, linear sessions nished 27% above fundamental price on average, concave sessions 23% below (p-value ). Di erence is still large (+21% vs. -18%) over second half of each session, but p-value is L2 is signi cantly di erent from all other treatments, the others are not signi cantly di erent from each other. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

33 Why large di erence between L2 and L3? L3 prices actually increased more than L2 prices during session on average (4.5 vs. 3 francs). Thus the di erence is due to a large di erence in initial prices (13.5 vs on average). Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

34 Why large di erence between L2 and L3? L3 prices actually increased more than L2 prices during session on average (4.5 vs. 3 francs). Thus the di erence is due to a large di erence in initial prices (13.5 vs on average). Mean risk tolerance was higher in L2 than in L3. Linear regression of mean B choices on initial price in linear sessions has coe cient 5.17 (p-value ) and R 2 of Linear regression of mean B choices on initial price in all sessions has coe cient 4.19 (p-value 0.002) and R 2 of Thus di erence between L2 and L3 is in part attributable to the distribution of risk tolerance in these sessions. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

35 Mean Session Risk Tolerance and Initial Prices Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

36 Consumption-Smoothing Finding 3: In the concave utility treatments there is strong evidence that subjects are using the asset to intertemporally smooth their consumption. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

37 Concave d = 2 sessions, per capita shares held by Type 1 Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

38 Concave d = 3 sessions per capita shares held by Type 1 Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

39 Consumption-smoothing behavior Proportion of periods Type 1 players buy (sell) shares if the period is odd (even) and Type 2 players buy (sell) shares if the period is even (odd). Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

40 Assets are Hoarded in Linear Sessions Finding 4: In the linear utility treatment, the asset is hoarded by just a few subjects. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

41 Assets are Hoarded in Linear Sessions Finding 4: In the linear utility treatment, the asset is hoarded by just a few subjects. Mean Gini coe cient for shareholdings in nal two periods of a session is 0.37 in all concave treatments (compared with 0.3 or lower in equilibrium). The Gini coe cient is 0.63 in all linear treatments (di erence between concave and linear p-value ). Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

42 Distribution of Mean Shares During Final Two Periods Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

43 Risk Tolerance and Shareholdings Finding 5: The more risk-tolerant subjects (according to the HL instrument) tend to accumulate more assets in linear sessions, but not in the concave sessions. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

44 Risk Tolerance and Share Accumulation - Evidence Random e ects regression of shares held during the nal two periods on HL scores (#B choices). Coe cient on #B choices is 0.46 in linear sessions (p-value 0.033) Interpretation - Every two additional B choices leads to nearly one extra share held on average during the nal two periods (per capita share endowment is only 2.5). Results nearly identical for xed e ects regression. Coe cient on B choices is in the concave sessions (p-value 0.407) We obtain similar results from random e ects regression of within-session rank of shareholders on HL scores. The highest and second highest ranked shareholders have average rank 8.3 (12=highest). Fixed e ects speci cation produces similar results. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

45 Results - Summary Relative to fundamental price / expected value, prices tend to be low when consumption-smoothing is induced via a concave utility function and high when with an induced linear utility function in otherwise identical economies. Most subjects smooth consumption in the concave sessions and rarely accumulate a large number of shares. The higher prices observed in the linear sessions are driven by a high share concentration among the most risk-tolerant subjects. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43

46 Some Further Extensions: Unpack the shock components of Hussam et al to gure out what is necessary to rekindle a bubble among experienced subjects. Gender di erences: SSW with all-female or all-male cohorts? Add an initial public o ering (IPO) of shares (rather than giving these away to subjects) at an initial price that is below the rst period fundamental value: do subjects buying shares in an IPO think harder about the asset s fundamental value over a T -period horizon? Fund management model (are n > 1 heads better than 1 / team behavior): One person forecasts price. Given this forecast, the other person makes an asset purchase decision (or some other consensus process). Test the capital-asset pricing model (CAPM) where assets are priced according to their sensitivity to non-diversi able risk β,under the assumption of mean-variance preferences. Asset Pricing Experiments: Bubbles, Crashes & Expectations BLEESSM June / 43